Spatiotemporal vehicle load modeling of bridges using statistical-informed denoising diffusion implicit model

Accurate spatiotemporal vehicle load modeling is critical for the safety assessment and fatigue analysis of bridges. However, vehicle loads exhibit stochastic characteristics in the spatiotemporal dimension, computing and modeling the joint distribution of such high-dimensional random sequences remains a challenging task. In this study, the statistical-informed denoising diffusion implicit model (DDIM) is proposed to generate spatiotemporal vehicle loads including time headway, gross weight, number of axles, and corresponding lanes. The proposed statistical-informed DDIM consists of two processes: (1) forward process, gradually adding noises to spatiotemporal vehicle loads until the noisy data approaches the standard Gaussian distribution; (2) generative process, removing noises predicted by U-Net and generating multi-lane vehicle loads conforming to actual spatiotemporal features through the non-Markovian process. Meanwhile, the relevant features based on the empirical distribution function (EDF) of vehicle loads are also included in the loss function to learn the statistical properties. Trained statistical-informed DDIM can directly generate similar spatiotemporal vehicle loads from random noises sampled in the standard Gaussian distribution. The proposed statistical-informed DDIM exhibits higher accuracy compared with the Monte Carlo simulation and other generative models.